Power series is one of the important concepts in mathematical analysis, which means that every term in the series is a power of (x-a), which is a constant multiple of the series number n (n is an integer counting from 0, and a is a constant). Power series is an important concept in mathematical analysis, which has been used as a basic content in many fields such as real variable function and complex variable function.

In mathematics, Taylor series is a series of infinite terms to represent a function, and these added terms are obtained by the derivative of the function at a certain point. Taylor series is named after British mathematician Brook Taylor, who published Taylor formula in 17 15. Taylor series derived from the derivative of a function at the zero point of the independent variable is also called McLaughlin series, which is named after the Scottish mathematician colin maclaurin. Taylor series plays an important role in approximate calculation.

The importance of Taylor series is reflected in the following three aspects:

Derivation and integration of power series can be carried out item by item, so the summation function is relatively easy.

Through analytic continuation, the analytic function can be extended to Taylor series defined in the open domain on the complex plane, thus making complex analysis possible.

Taylor series can be used to approximately calculate the function value.